Why is my lattice drastically deforming its mesh?
You must not scale your Lattice in Edit mode or it will completely screw the object it is linked to, as it's happening right now, because it takes all these scale deformations into account when you link your object to it. Make all the scales you need in Object mode. Then you can enter in Edit mode and move the vertices or scale to deform the object, but before that, keep the initial shape as a Shapekey so you can come back to it whenever you want. So I guess you have to delete and redo your Lattice.